After reading the paper, Graphing Calculators as Tools, briefly write what you understand regarding TPACK (technology, pedagogy, and content knowledge). If you have any questions regarding the topic, post those here on this page as well (you do NOT have to start a discussion).
This is due Thursday morning, 11/10, before class.
After reading the paper about TPACK, I can see how technology can be more beneficial in a middle school classroom. The article talked about how TPACK is more than the teacher having the knowledge of technology. It is more about the teachers knowing their students and how their students react to information, being able to integrate technology into the classroom. Additionally, I learned TPACK is all about integrating these together. It is one thing to know about technology and understand it, but it is not going to be beneficial for the students without understanding how.
What I got from the article was this technology will help students understand more. I look back at what I did when I was in middle school and I remember I was the only student with a graphing calculator and not even my teacher knew how to work it. This article taught me that it is my responsibility to know and integrate this technology into my class because no one is going to do it for me. I realize how I was taught trust the basics and not why and how. What I learned was very analytical and procedural. It is my job to make sure future students don't have to deal with this.
The section about the angle information was particularly interesting to be because even now, I don't have any idea how to work with angles on a calculator. I remember being in my middle school geometry class and no one needed their calculators because my teacher didn't find the need for them. I think, if I were to teach any form of middle school, all of these technologies could be not only beneficial but worthy of me getting to know and working on integrating into my classroom.
Questions: How do I learn about these and how to implement the technology? How do I get these technologies in my class?
Katey Cook
Reading the paper on TPACK, I know understand how electronic tools can heighten and individuals learning process in the classroom. It is up to the teacher to understand how their students are performing in the class and at which ways can technology help the learning process. The teacher must know when to incorporate technology into their classroom for the learning of mathematics so the students aren't just doing whatever they with the technology.
The graphing calculator is a helpful device. With it you can increase algebra skills, geometry and measurement, and data analysis and probability. This calculator has applications in it which can make these subjects easier to tackle. Along with the correct teaching instructions students can use the calculator to solve problems presented by the teacher. When i was in middle school i noticed my calculator had the probability app. I use to think of it as a simple game the calculator came with. It wasn't until i was in high school where I became aware that this program was helpful if i wanted to find the probability of rolling dice. If all students have an opportunity to work with graphing calculators I think it would make the mathematical thought in the classroom that much higher.
A few questions I pose are how to make tools like these accessible to students at home? I know the schools provides calculators for students in the classroom, but students are not allowed to take these tools outside the classroom. another question I pose is are there any other tools out there like the calculator that can benefit students learning? If so what are they?
Fredrick Martin
From my understanding, TPACK (technology, pedagogy, and content knowledge) combines the use of technology with the skills of being a teacher and our knowledge of our subject area. The goal of this is to develop and deepen our students' understanding of mathematical ideas. TPACK incorporates when, where, and how to use technologies. Instead of simply utilizing a graphing calculator to display routine graphs and tables, TPACK involves a number of alternate uses. With the growing influence of technology in the middle school classroom, this is a way to integrate new tools with the learning process. The article discussed utilizing a TI-73 calculator (designed specifically for middle school students) to make connections with topics in algebra, geometry, and data collection and probability. These tools can even save valuable classroom time; often it can be quicker to use a program on the calculator to demonstrate something rather than physical manipulatives. Personally, I did not know graphing calculators had many of the features mentioned in the article, specifically the angle programs and different types of probability devices. Since I tend to be a bit technologically challenged, I hope to be able to learn how to use these tools wisely and effectively in a way that enhances student comprehension of mathematics.
Questions I have: What is the best way to deal with the time delay that set-up and technological difficulties can create? Do most middle schools have a set of TI-73 calculators (or some other tools) for students to use, or would that be something for which we would need to either obtain a grant or request students to bring their own? What are the consequences of NOT involving technology with our educational practices?
Mandi Mills
From Dr. B’s article, TPACK is the interconnection and intersection of technology, pedagogy, and content knowledge (1-4). Teachers have to understand their students, the content they are teaching, and how the technology will further their students' understanding of the subject. Specifically the article mentions using a graphing calculator (TI-73) to investigate algebra, geometry, and probability. It’s true that graphing calculators have a number of abilities that can “amplify” the mathematics. With the calculator being able to connect to the CBRs, it allows students to physically explore the relationships of a graph of distance vs. time. Using calculators can enhance the learning of middle school students and allow them to take a hands-on approach in exploring different relationships in mathematics.
Questions I have about the use of calculators in the classroom include:
How many schools are equipped with graphing calculator sets now? Do most schools have CBRs and TI-73s?
I know that these rangers can be connected to computers, is there an advantage in using a calculator instead of a computer?
We briefly mentioned Vernier giving out grants for schools. How accessible are those funds to schools? What would I as a teacher have to do to attain a grant to enable my school to buy the CBRs and TI-73s?
Mike Freeland
With the advent of technology for personal use came a wave of products like smart phones, GPSs, and electronic readers. Now that we have search engines at our fingertips from morning until night, the questions asked by our brains in idle time seldom go unanswered, but what about questions that we ask during academic time? I can find directions from my house to the Washington monument in seconds and download any book that my heart desires to my kindle for the car ride there, but when I am stumped on a math problem, I must leaf through the pages in my textbook to find a helpful example. Though every other task in our lives seems to have been made simplified through technology, educational tasks have remained somewhat static. This is where the importance of TPACK becomes obvious. As technology has become a defining part of our lives, it must be present within mathematics classrooms for the subject to remain accessible and interesting. Pedagogy and content knowledge have always been a necessary part of a teacher’s repertoire, but teachers who effectively utilize technology in the classroom can greatly benefit their students. Routine tasks that would eat-up classroom time (like graphing something point by point) are simplified by a graphing calculator’s ability to collect and represent data quickly. Rather than just using graphing calculators to check sums, their applications like SMILE or the CBR component should be used as a springboard for classroom conversations. Really, we aren’t trying to teach to students how to graph something; the goal of using this technology is for students to understand and interpret what a graph means in terms of numbers and real-life situations. If they understand the concept, being able to graph something by hand will follow naturally.
Truthfully, I am perpetually afraid of becoming too dependent on technology. I imagine our world heading towards one similar to that imagined by Ray Bradbury. Which is why my question is this: Despite the positive attributes that technology has in terms of advancing understanding in mathematics classrooms, is it possible for students to see mathematics as something that is impossible without technology? When I ask my students to represent an angle or a fraction, I don’t want them always reaching for a calculator, when they could more simply point out the right angle in the corner of the room, or the fraction of the class that wears glasses. As I am in search of a way to incorporate technology without allowing it to become too predominant in my classroom, my next question is what is an appropriate balance?
Valerie Gipper
TPACK is a perfect blend of teaching, pedagogy, and content knowledge which, when used correctly, results in the effective use of technology in the classroom. TPACK allows for students to explore mathematics and contributes to greater understanding more than direct instruction . Technology in the classroom can be used to give students immediate feedback, allow them to look at more than one example, display graphs and charts, and collect and generate data. In my day, calculators only seemed to be used for calculating an answer. Now, it is clear that they can be put to much better use, which will benefit the student.
A few questions that come to mind- Are there other technologies, not mentioned in this article, that could be beneficial in the classroom? Are there inexpensive alternatives to the CBR? What grade level should these technologies first be introduced?
Hailey McDonell
From my understanding TPACK is the combination of technology, pedagogy, and content knowledge. In other words TPACK is the integration of technology in the classroom. This integration can prove fruitful if put into the hands of a specialist in the content area. Dr. B’s article gave the example of using graphing calculators and the CBR to help students relate distance and time. This method of teaching the standard y=mx+b gives a deeper meaning and understanding to the student. I think the main idea is that students today have such a deep connection to technology in most every aspect of their lives that not bringing technology into the classroom seems inappropriate. If a teacher is well versed in their content area as well as an expert at the introduced technology there is a better chance that students will obtain a better understanding of the chosen topic.
Where do I find these technologies? I didn’t know that graphing calculators could be connected to CBRs before this class so I wonder where would I find these ideas to implement into my classroom?
Christopher Cardon
The developments in calculation technology have lead to what is accessible to math classes today: tools that can calculate large numbers instantaneously, graph any function or linear system, and even simulate random number functions. Our job as teachers is not only to keep up with the ever changing world of technology, but to understand how the many applications they may have on lessons in the curriculum. One function of the calculator particularly useful involves linking it to at motion detector. This pedagogy gets students directly involved with their learning, enabling them to physically investigate linear relationships, rates of change, and other purposes as well. The graphs on the calculators are not longer just lists of numbers “L1 and L2”, but a visual representation of the rate of their movement. The slope of the line resembles the rate of change or speed rather than m, and the y-intercept can be seen as a starting point b (482-2).
This calculator function also efficiently generates/collects data and provides immediate feedback. The motion sensor is only one mind blowing thing technology has to offer in the mathematics classroom. Whatever neat tool comes around it is important to consider how you might incorporate it in a conceptually meaningful way (485-5).
This is due Thursday morning, 11/10, before class.
After reading the paper about TPACK, I can see how technology can be more beneficial in a middle school classroom. The article talked about how TPACK is more than the teacher having the knowledge of technology. It is more about the teachers knowing their students and how their students react to information, being able to integrate technology into the classroom. Additionally, I learned TPACK is all about integrating these together. It is one thing to know about technology and understand it, but it is not going to be beneficial for the students without understanding how.
What I got from the article was this technology will help students understand more. I look back at what I did when I was in middle school and I remember I was the only student with a graphing calculator and not even my teacher knew how to work it. This article taught me that it is my responsibility to know and integrate this technology into my class because no one is going to do it for me. I realize how I was taught trust the basics and not why and how. What I learned was very analytical and procedural. It is my job to make sure future students don't have to deal with this.
The section about the angle information was particularly interesting to be because even now, I don't have any idea how to work with angles on a calculator. I remember being in my middle school geometry class and no one needed their calculators because my teacher didn't find the need for them. I think, if I were to teach any form of middle school, all of these technologies could be not only beneficial but worthy of me getting to know and working on integrating into my classroom.
Questions: How do I learn about these and how to implement the technology? How do I get these technologies in my class?
Katey Cook
Reading the paper on TPACK, I know understand how electronic tools can heighten and individuals learning process in the classroom. It is up to the teacher to understand how their students are performing in the class and at which ways can technology help the learning process. The teacher must know when to incorporate technology into their classroom for the learning of mathematics so the students aren't just doing whatever they with the technology.
The graphing calculator is a helpful device. With it you can increase algebra skills, geometry and measurement, and data analysis and probability. This calculator has applications in it which can make these subjects easier to tackle. Along with the correct teaching instructions students can use the calculator to solve problems presented by the teacher. When i was in middle school i noticed my calculator had the probability app. I use to think of it as a simple game the calculator came with. It wasn't until i was in high school where I became aware that this program was helpful if i wanted to find the probability of rolling dice. If all students have an opportunity to work with graphing calculators I think it would make the mathematical thought in the classroom that much higher.
A few questions I pose are how to make tools like these accessible to students at home? I know the schools provides calculators for students in the classroom, but students are not allowed to take these tools outside the classroom. another question I pose is are there any other tools out there like the calculator that can benefit students learning? If so what are they?
Fredrick Martin
From my understanding, TPACK (technology, pedagogy, and content knowledge) combines the use of technology with the skills of being a teacher and our knowledge of our subject area. The goal of this is to develop and deepen our students' understanding of mathematical ideas. TPACK incorporates when, where, and how to use technologies. Instead of simply utilizing a graphing calculator to display routine graphs and tables, TPACK involves a number of alternate uses. With the growing influence of technology in the middle school classroom, this is a way to integrate new tools with the learning process. The article discussed utilizing a TI-73 calculator (designed specifically for middle school students) to make connections with topics in algebra, geometry, and data collection and probability. These tools can even save valuable classroom time; often it can be quicker to use a program on the calculator to demonstrate something rather than physical manipulatives. Personally, I did not know graphing calculators had many of the features mentioned in the article, specifically the angle programs and different types of probability devices. Since I tend to be a bit technologically challenged, I hope to be able to learn how to use these tools wisely and effectively in a way that enhances student comprehension of mathematics.
Questions I have: What is the best way to deal with the time delay that set-up and technological difficulties can create? Do most middle schools have a set of TI-73 calculators (or some other tools) for students to use, or would that be something for which we would need to either obtain a grant or request students to bring their own? What are the consequences of NOT involving technology with our educational practices?
Mandi Mills
From Dr. B’s article, TPACK is the interconnection and intersection of technology, pedagogy, and content knowledge (1-4). Teachers have to understand their students, the content they are teaching, and how the technology will further their students' understanding of the subject. Specifically the article mentions using a graphing calculator (TI-73) to investigate algebra, geometry, and probability. It’s true that graphing calculators have a number of abilities that can “amplify” the mathematics. With the calculator being able to connect to the CBRs, it allows students to physically explore the relationships of a graph of distance vs. time. Using calculators can enhance the learning of middle school students and allow them to take a hands-on approach in exploring different relationships in mathematics.
Questions I have about the use of calculators in the classroom include:
How many schools are equipped with graphing calculator sets now? Do most schools have CBRs and TI-73s?
I know that these rangers can be connected to computers, is there an advantage in using a calculator instead of a computer?
We briefly mentioned Vernier giving out grants for schools. How accessible are those funds to schools? What would I as a teacher have to do to attain a grant to enable my school to buy the CBRs and TI-73s?
Mike Freeland
With the advent of technology for personal use came a wave of products like smart phones, GPSs, and electronic readers. Now that we have search engines at our fingertips from morning until night, the questions asked by our brains in idle time seldom go unanswered, but what about questions that we ask during academic time? I can find directions from my house to the Washington monument in seconds and download any book that my heart desires to my kindle for the car ride there, but when I am stumped on a math problem, I must leaf through the pages in my textbook to find a helpful example.
Though every other task in our lives seems to have been made simplified through technology, educational tasks have remained somewhat static. This is where the importance of TPACK becomes obvious. As technology has become a defining part of our lives, it must be present within mathematics classrooms for the subject to remain accessible and interesting. Pedagogy and content knowledge have always been a necessary part of a teacher’s repertoire, but teachers who effectively utilize technology in the classroom can greatly benefit their students. Routine tasks that would eat-up classroom time (like graphing something point by point) are simplified by a graphing calculator’s ability to collect and represent data quickly. Rather than just using graphing calculators to check sums, their applications like SMILE or the CBR component should be used as a springboard for classroom conversations. Really, we aren’t trying to teach to students how to graph something; the goal of using this technology is for students to understand and interpret what a graph means in terms of numbers and real-life situations. If they understand the concept, being able to graph something by hand will follow naturally.
Truthfully, I am perpetually afraid of becoming too dependent on technology. I imagine our world heading towards one similar to that imagined by Ray Bradbury. Which is why my question is this: Despite the positive attributes that technology has in terms of advancing understanding in mathematics classrooms, is it possible for students to see mathematics as something that is impossible without technology? When I ask my students to represent an angle or a fraction, I don’t want them always reaching for a calculator, when they could more simply point out the right angle in the corner of the room, or the fraction of the class that wears glasses. As I am in search of a way to incorporate technology without allowing it to become too predominant in my classroom, my next question is what is an appropriate balance?
Valerie Gipper
TPACK is a perfect blend of teaching, pedagogy, and content knowledge which, when used correctly, results in the effective use of technology in the classroom. TPACK allows for students to explore mathematics and contributes to greater understanding more than direct instruction . Technology in the classroom can be used to give students immediate feedback, allow them to look at more than one example, display graphs and charts, and collect and generate data. In my day, calculators only seemed to be used for calculating an answer. Now, it is clear that they can be put to much better use, which will benefit the student.
A few questions that come to mind- Are there other technologies, not mentioned in this article, that could be beneficial in the classroom? Are there inexpensive alternatives to the CBR? What grade level should these technologies first be introduced?
Hailey McDonell
From my understanding TPACK is the combination of technology, pedagogy, and content knowledge. In other words TPACK is the integration of technology in the classroom. This integration can prove fruitful if put into the hands of a specialist in the content area. Dr. B’s article gave the example of using graphing calculators and the CBR to help students relate distance and time. This method of teaching the standard y=mx+b gives a deeper meaning and understanding to the student. I think the main idea is that students today have such a deep connection to technology in most every aspect of their lives that not bringing technology into the classroom seems inappropriate. If a teacher is well versed in their content area as well as an expert at the introduced technology there is a better chance that students will obtain a better understanding of the chosen topic.
Where do I find these technologies? I didn’t know that graphing calculators could be connected to CBRs before this class so I wonder where would I find these ideas to implement into my classroom?
Christopher Cardon
The developments in calculation technology have lead to what is accessible to math classes today: tools that can calculate large numbers instantaneously, graph any function or linear system, and even simulate random number functions. Our job as teachers is not only to keep up with the ever changing world of technology, but to understand how the many applications they may have on lessons in the curriculum. One function of the calculator particularly useful involves linking it to at motion detector. This pedagogy gets students directly involved with their learning, enabling them to physically investigate linear relationships, rates of change, and other purposes as well. The graphs on the calculators are not longer just lists of numbers “L1 and L2”, but a visual representation of the rate of their movement. The slope of the line resembles the rate of change or speed rather than m, and the y-intercept can be seen as a starting point b (482-2).
This calculator function also efficiently generates/collects data and provides immediate feedback. The motion sensor is only one mind blowing thing technology has to offer in the mathematics classroom. Whatever neat tool comes around it is important to consider how you might incorporate it in a conceptually meaningful way (485-5).
- Tim H.